Impact yielding of high density polyethylene

Impact yielding of high density polyethylene B. J. Briscoe and I. M. Hutchings Physics and Chemistry of Solids, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, UK (Received 14 May 1976; revised 23 July 1976) We have used a projectile impact method to estimate the flow stress of high density polyethylene at a strain rate of ~3 x 103 sec-1. The technique was developed initially by Taylor and applied successfully by Whiffin and others to ductile metals. The data from this experiment have been compared with data obtained in more conventional compression and drop hammer tests at lower strain rates at 20 ° and 100°C. The flow stress of high density polyethylene deduced from the impact test at 20°C is significantly higher than that anticipated from a simple extrapolation of the low strain rate data at 20°C. The data at 100°C are however in good agreement. The technique has also been used to estimate the flow stress of high density polyethylene as a function of temperature over the range - 2 0 ° to +105°C. These data indicate that the discrepancy in the data for 20°C arises from a real discontinuity in the response of the polymer rather than from an inadequacy in the theoretical analysis of the impact experiment as applied to polymeric solids. We conclude that the impact method described is a useful technique for estimating the flow stress of polymers. It is however limited to a relatively narrow range of strain rates.

INTRODUCTION A deformable cylinder (Figure la) impacted axially against a rigid plane at a high velocity will suffer permanent deformation. In the case of an ideal rigid-plastic material the deformation is of the form shown in Figure lb. For this case Taylor 1 showed that the yield stress, o, of the material may be estimated from the geometry of the impacted specimen, using the following formula: o "~

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(1)

where (Figure 1)0 is the density of the specimen; V is the impact velocity; L 0 is the original length of the cylinder; L is the ffmal length and X is the length of the undeformed portion of the cylinder. The mean rate of strain, ~, during the impact was shown ~ to be

~- V[2(Lo - X)

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Equation (1) has been used successfully by Whiffin 2 and others to estimate the flow stress of metals at high strain rates. Taylor's analysis was based on a momentum exchange calculation for an ideal rigid-plastic material; more recent treatments 3'4 which take account of strain hardening and elastic deformation predict yield stresses which differ only slightly from the value given by equation (1). We have used Taylor's method to estimate the yield stress of high density polyethylene at a mean strain rate of about 3 × 10 3 sec - 1 . . The result is compared with mea* Although in principle the strain rate may be readily varied by changing the impact velocity, in practice at low velocities the deformation is too small for accurate measurement, and at high velocities it is too gross for the theoretical assumptions to be valid. The usefulness of the method is therefore restricted to strain rates of around 3 X 103 sec-1 for high density polyethylene.

surements obtained by uniaxial compression in conventional compression tests and drop-weight impact tests at lower strain rates (up to 3 x 102 sec-1). The projectile impact experiment gives a yield stress significantly higher than that anticipated from a simple Eyring extrapolation of the lower strain rate data. The reason for this anomaly is uncertain; it may be due either to a real change in yield properties of the polymer at these high rates of strain or to an inadequacy in the interpretation of the impact response of polymers using the Taylor method. This impact method has also been used to study the apparent yield stress of high density polyethylene over the temperature range - 2 0 ° to +105°C. While the yield strength decreases rapidly with temperature the variation cannot be simply explained using an Eyring flow model. EXPERIMENTAL

Taylor impact method A commercial grade of high density polyethylene (Rigidex 075-65) was used in the form of 16 mm diameter rod (density 953 kg/m3). Plane-ended cylindrical specimens ~40 ram in length were accelerated using a compressed-gas gun s and allowed to impact axially against a massive smooth-faced steel anvil. Two high speed photographic sequences are shown in Figure 2. Figure 2a shows the impact for a typical velocity (120 m/sec) at 100°C and thus corresponds to the maximum observed deformation of the cylinder. The surface of the cylinder was lubricated with MoS2 grease to reduce frictional losses during impact. The impact velocity was about 110 m/sec and was measured to within 1% by timing the interruption of two light beams crossing the barrel 6. The polymer specimens could be heated before impact by means of an electrical heating element around the breech of the gun. The temperature of the barrel surface immed-

POLYMER, 1976, Vol 17, December 1099

Impact yielding o f high density polyethylene: B. J. Briscoe and I. M. Hutchings

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to +100°C and 90 to 125 m/sec. The rebound energy was therefore ~7% of the initial kinetic energy of the projectilet The final dimensions of the specimens were measured with a micrometer screw gauge. The impacted specimens showed various degrees of concavity on the impacted surface. This is shown schematically in Figure lc. In all cases the length L was measured along the axis of the cylinder. The concavity becomes more extreme at the highest impact temperature where AL/(L 0 - L ) approached 0.8. Figure 2b shows the rebound of a specimen impacted at 100°C and at a velocity of 170 m/sec. The deformation of the cylinder is extremely pronounced and indeed much greater than observed in cylinders where yield stress measurements were made. At this velocity the concavity of the specimen end is accentuated. The photographs indicate that this concavity, AL, is produced as the cylinder rebounds from the anvil; the axial length L remains sensibly constant during rebound. It is not clear why this postimpact deformation occurs but it may be due to a combination of factors including momentum effects, hydrostatic effects and elastic recovery. The mean flow stress and the mean rate of strain were calculated from equations (1) and (2). After impact several specimens were cut along their axes and sections of the cylinder were microtomed. These sections were examined for stress birefringence and local tensile failure.

Hammer impact method The instrumented drop-weight apparatus described by Heavens and Field 7 was used. The measurements were carried out at 20°C and the mean calculated strain rate w a s

t No correction was made for this effect in the data quoted below. At present the theoretical treatment of such a correction is unclear. However a simple argument suggests that the calculated valuesof a (equation 1) might be reduced by up to 7%.

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Figure 1 Projectiles used for the Taylor impact experiment: (a) before impact; (b) after impact; (c) shows the concavity which forms after impact at 100°C. This concavity is less pronounced at lower temperatures

lately above the specimen was measured by means of a thermocouple; the reading of this thermocouple was compared in a series of calibration experiments with the temperature measured by a thermocouple at the centre of a dummy polyethylene cylinder in the barrel when a steadystate temperature had been achieved. In all experiments at elevated temperatures the specimen was allowed to reach thermal equilibrium in the heated breech for 15 min before firing; we estimate that with these precautions the quoted temperatures are accurate to +2K and that the maximum non-uniformity of temperature is of a similar order. A few experiments were performed at below room temperature, in which specimens were cooled in a refrigerator before firing; the estimated temperature of -20°C is accurate to only + 1OK. In some experiments the rebound velocity was measured by a similar photoelectric timing method to the one described above; the rebound velocity was found to be 30 --- 2 m/sec and to be essentially independent of specimen temperature and impact velocity over the range - 2 0 ° C

1100 POLYMER, 1976, Vol 17, December

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b Figure 2 Two sequences of high speed photographs; interframe time 19 #sec. Frames are numbered sequentially. Initial impact is from right to left. (a) Impact of a HDPE cylinder at 100°C and 120 m/sec. Cylinder diameter 16 mm. (b) Rebound of an HDPE cylinder after impact at 100°C and 170 m/sec. Elastic recovery and formation of the concavity on the impacted face occur between frames 1 and 5; the projectile breaks contact between frames 5 and 6. Rebound velocity 30 m/sec

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Loglo Figure 3 Flow stress of high density polyethylene measured by several techniques, plotted against log (strain rate) for two different temperatures: A, 20°C; B, 100°C. Note the sudden increase in flow stress at 20°C above ~ = 3 X 102, which does not appear in the results at 100°C. This work: E3, uniaxial compression; V, drop-weight; O, Taylor impact uniaxial compression: O, Amuzu and Briscoell;ll Bowden and Jukes s

~3 x 102 sec -1. The specimens were cylindrical and somewhat smaller than those used in the impact tests (diameter 6 mm, length 6 mm) and a certain amount of barrelling was detected in the deformed specimens.

Low strain rate tests Low strain rate compressive tests were carried out using a commercial testing machine (Instron) in the range 10 -3 to 1 sec -1. The yield stress was taken to correspond to 10% strain following Bowden and Jukes 8.

EXPERIMENTAL DATA AND DISCUSSION

Figure 3 shows our data and that of other workers for the influence of strain rate, ~, on the compressive flow stress, o, of various grades of high density polyethylene at 20 ° and 100°C. Following the classical analysis based on the high stress limit of an Eyring-type stress-modified thermally activated flow process 9'1° we have plotted lOgl0 e against o. With the exception of one data point, that for Taylor impact at 20°C, the data for each temperature show a similar monotonic increase in the value of a with increasing values of logl0 e. It appears that the Taylor impact technique gives a reasonable value of cr at 100°C. However the value of o calculated from the impact technique at 20°C is at least twice that anticipated from the linear extrapolation of the low strain rate data. This discrepancy seems to arise from a change in the mode of deformation of the polymer at strain rates above about 3 × 102 sec - I at 20°C. There is evidence for this in the stress birefringence of the sections of polymer cut from the impacted specimen. At 20°C the impact specimen shows a diffuse region of deformation which penetrates into the cylinder to a depth of the order of one quarter of the diameter of the cylinder. At 100°C however the deformation is more localized in a region close to the impact surface and penetrates to a depth of only about one eighth of the diameter. In addition these specimens show evidence of gross tensile rupture close to the impact surface. The deformation observed at 100°C was with the exception of the gross failure region very similar to that obtained in the slip region during conventional compression tests at both 20 ° and 100°C.

A change in the mode of deformation at the high impact strain rates is also indicated by a marked difference in the temperature dependence of the flow stress at high and low strain rates. In Figure 4 we show our data for the temperature dependence of the flow stress at two strain rates. In both cases the flow stress decreases linearly with temperature. However the temperature dependence at the high strain rate is about three times greater than at the low strain rate. In Figure 4 we show low strain rate data for ~ = 20 sec -1 . Similar temperature dependences have been observed at strain rates down to 1 sec-11~. At about 100°C the higher strain rate data (by the impact technique) are very similar to the lower strain rate uniaxial compression data. It is not clear from the present data whether the results at the two strain rates become coincident or cross over at about 100°C. The data obtained from the impact technique become very inaccurate above 120°C due to excessive concavity in the impacted specimens and thus this question cannot be answered using Taylor's method. However these data do indicate that the discontinuity in the logl0 e against o plot at 20°C (Figure 3) is due to a change in the physical properties of the polymer rather than to an artefact inherent in the impact technique. We have no unequivocal explanation for the discontinuity or for the different temperature dependences. The onset of crystallite melting occurs at about 100°C in high density polyethylene. It therefore seems that these effects are associated with the crystalline nature of high density polyethylene. Ia the absence of data at higher strain rates and temperatures it is probably not sensible to speculate on their origin. Nevertheless the data do indicate that the Taylor iropact technique forms a useful method for estimating the flow stress of polymers, although unfortunately limited to a very narrow range of strain rates.

ACKNOWLEDGEMENTS We thank Professor D. Tabor for his support and encouragement during the course of this study. We are also grateful for the award of Research Fellowships from the Oppenheimer Fund (B. J. B.) and St. John's College, Cambridge (I.M.H.).

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P O L Y M E R , 1976, V o l 17, December

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Impact Fielding of high density polyethylene: B. J. Briscoe and I. M. Hutchings REFERENCES 1 2 3 4 5

Taylor, G. I. Proc. R. Soc. (A} 1948, 194, 289 Whiffin, A. C. Proc. R. Soc. {A) 1948, 194,300 Hawkyard, J. B. lnt. J. Mech. Sci. 1969,11,313 Lee, E. H. and Tupper, S. J. J. Appl. Mech. 1954, 21, 63 Hutchings, I. M. andWinter, R. E. J. Phys. [EJ 1 9 7 5 , 8 , 8 4

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Hutchings, 1. M. Rev. ScL Instrum. in press Heavens, S. N. and Field, J. E. Proc. R. Soc. (A} 1974, 338, 77 Bowden, P.B. and Jukes, J . A . J . Mater. Sci. 1 9 7 2 , 7 , 5 2 Ward, l . M . J . Mater. Sci. 1971,6,1397 Bauwens-Crowet, C., Bauwens, J. C. and Homes, G. J. Polym. Sci. (A,2) 1969, 7,735 Amuzu, J. K. A. and Briscoe, B. J. unpublished data